[helene_t]

The first p with whom I played in a club found it strange that I, as a mathematician, couldn't count to 13. This is a ridicolous kind of bafflement of course, since mathematicians have learned to add and subtract Greek letters only, there is no reason to think a mathematician would be able to count. Anyway, for a bridge player it is a good thing to be able to.

I used to (to be honest, I still) do it like this: there have been played two round of this suit, that is eight. Oh one of the other players showed out on the second round, so seven. Someone (probably me) discarded a card of that suit, so eight. I have one card left in that suit and there are two in the dummy, that makes 11. 13-11=2. So p and declarer have two cards combined. Oh it was p who showed out. So declarer has two cards left.

Now I have read in several books that that is the way beginners usually try to count and it's not the way to do it. Yet I haven't seen anywhere a description of how the right way to do it is. Except in the special case where declarer and/or p (and thereby both) have shown there excact distribution in the auction (or the auction combined with the first one or two rounds).

I suppose that as soon as the dummy is open I should calculate the number of cards remaining in the two closed hands, and then whenever a spade is played by one of the closed hands, I subtract one from the number of outsstanding spades etc. If the distribution of one suit is known then I count that suit seperatly, keeping track of the number of cards holds and the number of cards declarer holds, rather than the sum of the two.

Is that right or is there a better way? Should I sometimes just count the two suits that matter or should I always try to count the entire hand?

[mcphee]

How about this plan. Lawrence has 2 CD's on Counting at Bridge and both are excellent products for the learning player. You can order these from the BBO bridge products. I reccomend these strongly to all students.

[ralph23]

All of Mike Lawrence's materials are very good IMO and the Counting At Bridge is no exception. FWIW, a method I use (maybe others do) is basically this (assume you're declarer):

Determine the number of cards the defenders hold collectively in suit X.

Imagine how those can be divided. You of course know the basic probabilities of suit breaks so you can rank these in effect. So make a working hypothesis. (E.g. "they are divided 3-2").

Eventually that hypothesis will either be proved or falsified; either way you will know.

I don't know if that makes sense; I may not be explaining it very well. But it's easier to count down than count up, imo.

[helene_t]

Tx Ralph and McPhee.

Yes, as delcarer it usually works that way. My problem is for example when I'm defending and declarer carries out a pseudosqueeze. It feels kinda stupid to discard the only menace and hold on to, e.g., two cards in a suit in which declarer has only one, when the defense only need one trick.

Paradoxically it feels easier to count as declarer - I say paradoxically because defenders usually have more information from the auction. I suppose it's because as declarer I sorta control the hand, I can decided roughly what suits are played first, and I know what suits and what cards are critical. Sometimes when I play 1NT with 14 combined points it feels like defending in the sense that at some point I totally lose the idea about what suits are still out.

[vang]

do not count, use pattern recognition. just know by heart the distribution table (4333, 4432, 5332 etc) and after each trick visualize possible distributions. i think this is recommended explained better in some books (anyone?).

[ralph23]

vang, on Oct 10 2007, 11:09 AM, said:

do not count, use pattern recognition. just know by heart the distribution table (4333, 4432, 5332 etc) and after each trick visualize possible distributions. i think this is recommended explained better in some books (anyone?).

Yea, this is what I was trying to say, but vang articulated it considerably better. Make a tentative pattern hypothesis(es) and then try to verify/falsify it.

Also get clear with your regular partners on when to give count as defenders... you can play Count Discards if you like -- although I don't care so much for them myself.

[blackshoe]

As others have said, look for patterns. I would start by counting one hand - declarer's if you're defending, the defender about whose hand you know more, or which seems most important, if declaring. When that becomes easy (!) start thinking about the other unknown hand.

[barmar]

I also recommend looking for patterns. As you gain experience, you'll notice that these patterns show up all the time, and they should become part of the way you "think bridge". It starts when you pick up your own hand: you sort it into suits, count your HCP, and look at the shape (is it a boring 4333, or a shapely 5431?). Then listen to the bidding, and try to picture the likely shapes of the hands that partner and the opponents are describing.

Since there are both 13 cards in a hand and 13 cards in a suit, these same patterns also apply to the distribution of cards in a suit around the table. So if you get to know them, you just have to watch how many times a player follows suit, and catch their discards, and you should be able to work out which patterns are possible. Combine this with what you may have inferred from the auction and you've got it!

Keeping track of spot cards -- that's the toughie!

[mikeh]

Helene, don't feel badly about the way you count It's the way I count as well!

Yes, when I am considering a suit that either I will be attacking or that I am concerned the opps will be attacking, I do think of the various shapes that are possible, and I do try to construct the hidden hands in terms of shape. However, when it comes to tracking the cards played in a suit, and thus the remaining number of cards, I do it the old-fashioned, beginner's way of counting the cards played one card at a time.

I have read that, for example, when missing 5 cards in a suit, consciously hold in your head 5=0, 4=1 and 3=2 as patterns, both ways, and eliminate 5=0/0=5 when both follow and 4=1/1=4 when both follow to the second round, but that seems to me to be too much work

It may be that I am doing this pattern thing subconsciously... and that I've been playing for so long that the part of me that keeps track of these things is no longer something I think about or can even think about consciously...like riding a bicycle...if you have to think about what you are doing, you'll fall off. But it certainly seems to me that I count one card at a time while building pictures of hands.

[EricK]

It always seems to me that there is just too much information to remember in order to accurately build up a picture of the hands. So only people whose brain is wired in just the correct way can ever really do it.

Let's say you are declarer. The first thing you do is see how many cards are outstanding in each suit. You need to remember these as the hand progresses. Then, as a few tricks are played you will discover how one suit breaks, so you remember that. You will also probably have seen a discard in another suit. Now you not only have to remember this discard, but you also have to adjust your memory of how many cards are outstanding in that suit. But also, when somebody shows out of a suit, not only do you know how the suit breaks, you also discover how many cards his partner still holds. And this is another thing you need to remember - if you lose track of that, then at the end of the hand you might know that he had eg 5 spades to begin with but you won't know if he still has any left. And this is ignoring the rank of the cards outstanding. Is your ♦8 good? Well if there are still ♦s outstanding you need to know if any of them are higher.

And of course, even if you can manage all this and accurately build up a picture of what each defender holds, to work out the winning line you still have to be able to hold that picture solidly enough in your head that you can try out various play options in your mind without mixing this up with the reality of what tricks have actually been played.

[hrothgar]

At times, I've played Blackjack fairly seriously in Casinos. There wasn't a single time that I walked into a casino "cold". I always made sure to prepare extensively in advance. The initial stage of this preparation was practicing with a Blackjack counting program. (For what its worth, I think that having your brain wired right only matters at the very top levels. For most of us, nothing substitutes for practice)

These programs randomly generate a large shoe. They then start flash cards in front of you. Periodically the program quizzes you and asks you to provide the current count, estimate penetration, and provide the adjusted count.

Conceptually, it would be quite easy to write something similar for bridge. The program would randomly deal four hands. (You would only get to see your own hand) The program would then play out the hand - following suit when appropriate. Periodically, the program would quiz you and ask relevant questions.

I think that this type of application might prove useful for an anti-social wanker who really wanted to master counting. It should also be quite easy to code. (Obviously, you'd need something a bit more sophisticated if you wanted to extract inferences from the auction).

If anyone ever wanted to add a touch of "realism", you could tie this into BBO. BBO could extract the ordering of cards from real hand records. Potentially, you could even leverage the bidding (obviously, there would be some danger if folks were playing anything weird)

[barmar]

Yes, it's alot to remember, as Eric says. If it were easy, we wouldn't find the game so interesting.

However, it's best not to think of this as lots of random facts to remember, it should be part of a process of playing the hand. When dummy comes down, the first step is planning how you're going to play, and this usually includes making some assumptions about distributions, who has which high cards, etc. As the play progresses, you're constantly updating your knowledge and revising the plan.

I think you'll overload your memory if you try to keep track of little details. Instead, think of the big picture, the hand as a whole. It should be easier to remember "LHO appears to have 5332 distribution" or "both defenders have followed to 2 rounds of ♣" than trying to remember each card.

[awm]

I count roughly the way Mike and Helene do too...

Generally I try to remember every card that has been played. I try and do this trick by trick, which helps to remember the suits even if I lose track of the spot cards. There are times I will use this information to reconstruct the hand patterns (so as to compare what I've seen to what is known from the bidding).

My observation has been that this works great when I'm awake. But when I'm tired it seems like spot cards just go by in a blur and I can't reconstruct them...

[Mbodell]

I think one of the main advantages of counting "by pattern" rather than by card or round of a suit is that it fits best with the bidding and with the rest of the hand.

Also you may be able to tell better when you know all of a players pattern. If you just count one suit you may know "there are 3 cards left out" in this suit and not realize that LHO must have all 3 becuase RHO has 5 in one suit and 4 in some other and you know his pattern must have been something else.

[helene_t]

mikeh, on Oct 10 2007, 09:54 PM, said:

I have read that, for example, when missing 5 cards in a suit, consciously hold in your head 5=0, 4=1 and 3=2 as patterns, both ways, and eliminate 5=0/0=5 when both follow and 4=1/1=4 when both follow to the second round, but that seems to me to be too much work

It may be that I am doing this pattern thing subconsciously... and that I've been playing for so long that the part of me that keeps track of these things is no longer something I think about or can even think about consciously...like riding a bicycle...if you have to think about what you are doing, you'll fall off.

That is my impression as well, that trying to let my inner voice repeat the complete information "5-6-2-3, declarer showed out in diamonds, partner has even count spades, AJ - KQJ - Q - J" is just too much and may be counter-productive because when some of the information gets blured by memory errosion, the whole house collapses and I'm left with utter perplexity. Then it may be better to rely on subconscious registration ("I somehow feel that declarer has only one diamond left").

A similar issue relates to suit combinations. In simple cases I can analyze all possible scenarios, consider implications (tempo, avoidance, entries) of alternative strategies, compute probabilites, and make my choice. In more complex situation I just follow my intuition, which gets better and better with experience. Has the added advantage that table-precesnce things like opps tanking are factored in.

[Free]

I usually count in pattern. How suits split, what's been played so far, how many the defenders had in the beginning of the hand. All this combined gives you a pretty accurate picture of the hand at low costs. (also HCP are useful of course)

Counting card by card like you describe is a lot more waste of energy, but it works equally well...

In Berry Westra's book "Analyse 1" he describes this method. I'm not a Berry fan, but this has helped me improving my game.

[brianshark]

I kinda just count the tricks. Round of diamonds, so that's 4 gone. Another round, p showed out, 7 gone. I'm holding 3. Dummy has one. Dec must have 2 left. I usually can just remember who showed out when. And later in the deal, I just go by how many more or less I have in that suit than declarer. I had an extra diamond so I can pitch one safely. I had two less trumps so force him twice and I have trump parity.

I also keep track of honours played but on a suit by suit basis rather than trick by trick. (But usually not to hard to recall who played what if needs be.) I also find it easy to transfer to high spots if honours get captured en masse if I'm concentrating properly.

So if I want a hand pattern analysis or missing honour placement analysis, I recall the hand so far using the above counts and calculate those also using inferences from bidding, the way declarer played the hand and suit preference signals from my p.

I'm not great at picking up on partner's count signals though. Probably my biggest fault as a defender.

[jillybean]

I know I need to improve my counting but I am finding its not good enough to simply count tricks. I need to know which spots are out, has the 6 gone, is it safe to play my 5?
I think visualizing patterns is most helpful in planning the play, counting is critical to establish a suit but when you get down to the nitty gritty and overtricks you have to know which cards remain. I just dont know how other than complete focus and concentration.

[ArtK78]

helene_t, on Oct 10 2007, 08:48 AM, said:

The first p with whom I played in a club found it strange that I, as a mathematician, couldn't count to 13. This is a ridicolous kind of bafflement of course, since mathematicians have learned to add and subtract Greek letters only, there is no reason to think a mathematician would be able to count. Anyway, for a bridge player it is a good thing to be able to.

This is very funny. My regular partner is a mathematician, and he has trouble adding and subtracting.

Now, if a problem involves game theory or operations research, he is OK with that.